[LazyPup]

Where you say "going into the valve" i assume you mean the shaft from the handle that goes into the valve body. At the base of that shaft you should see a nut, called the stem packing nut. Under that nut there is a rubber or fibre packing that seals the shaft of the handle.

If you hold the body of the valve tight so it can not turn, you should be able to tighten the packing nut with another wrench. Tightening the nut expands the packing washer against the shaft and should stop the leak.

The copper water line is attached to the vavle by means of a compression fitting. Again, hold the body of the valve to steady it and tighten the nut. That should resolve your problem.